Multivariate Sobel-Uppuluri-Galambos-type bounds


E. Seneta and T. Chen


Research Report 99-17
Date: 2 August 1999


The upper and lower bounds in a recent multivariate generalization (Galambos and Xu,1996) of the univariate Sobel-Uppuluri-Galambos inequalities are shown to be weighted averages of individual multivariate bounds, and hence can be sharpened by optimizing over these individual bounds. Examples are used to illustrate the difference between bounds of this kind, and the kind of multivariate bounds appearing in Chen and Seneta(1996) and Galambos and Lee (1994). The difference in kind turns on the nature of extension of the idea of degree from univariate to multivariate.

Key phrases

Bonferroni-type inequality. degree. Meyer's identity. multivariate. optimization. weighted average.

AMS Subject Classification (1991)

Primary: 60E15
Secondary: 62H15


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